In the field of petroleum exploration, images of the Earth's subsurface are required for reservoir exploration and development. Seismic images of a subsurface region of the Earth created with different subsets of the recorded seismic data are often misaligned. FIG. 1 is an example illustration of an image of the Earth's subsurface resulting from seismic data recorded at different offsets. The solid lines represent the seismic image using near-offset seismic data; the dashed lines represent the image produced by far offset seismic data. These misalignments are usually caused by incorrect seismic velocities which produce distorted, unfocused subsurface images. Measured misalignment values can be analyzed to correct these velocities. This analysis is most often done by traveltime tomography, which compares recorded data to the results of forward modeling, or by the related process of migration velocity analysis, which compares the misalignments between migrated images, as is depicted in FIG. 1.
Standard traveltime reflection tomography methods include forward modeling to match synthetic data computed from an earth model to real recorded data. This match is achieved by making incremental changes to the earth model to find the velocity model that minimizes the mismatch between the reflection-event traveltimes of modeled and recorded data. A common way of correcting the misalignment is to raytrace from representative reflectors and use travel times along the rays to find velocity corrections that will best align modeled and real data. Likewise, migration velocity analysis analyzes traveltimes and velocities along reflection rays to bring the images from all offsets into alignment. Most often, the velocity corrections are calculated on a grid, such as is shown in FIG. 1. Rays are traced very densely from many reflection points along many reflection horizons. This raypath information is used to calculate the correction to the velocity model required in each grid cell to minimize the misalignments between the images from different data offset ranges.
Conventional traveltime reflection tomography and migration velocity analysis methods include reflector structure as part of the starting velocity model. This reflector structure might be interpreted horizons or could be a field of local dip measurements of an existing seismic image. In either case, the reflector structure will be uncertain where the image is degraded. The raypaths are very sensitive to the reflector structure: small changes in the dip of the reflector often cause the rays to go in greatly different directions. Moreover, multipathing of rays often occurs where seismic images are degraded. Thus, where the image is most in need of correction, the travelpath information needed to make the corrections is most uncertain. If the dip of the reflector is changed only slightly at the reflection point of a ray, the reflected part of the ray path will often be greatly changed to pass through a very different set of grid cells and thereby alter the inversion. A ray can also be very sensitive to other small-scale heterogeneity encountered along its path. This sensitivity is an artifact of the ray-based analysis, and is one of the primary reasons for current emphasis in the industry on wave-equation based inversions for developing accurate velocity models, even though such wave-equation methods lose much of the very useful geometric information provided by rays.
Instead of abandoning rays, and using wave equation methods, there is a need for a method that can combine the advantages of both to improve earth model seismic velocities and the resulting seismic images. In particular, there is a need for a traveltime reflection tomography method that is less sensitive to minor details of the velocity model, does not require an assumed reflector structure and works where reflection events are faulted and difficult to map as reflection surfaces.